Question

In a two digit number, digit at the tens place is twice the digit at units place. if the number obtained by interchanging the digits is added to the original number, the sum is 66. find the number​

Answer 1

Answer:

42

Digit at unit place = 2

Digit at tens place = 2 × Digit at unit place = 4

The two digit number = 42

The two digit number after interchanging the digits = 24

42 + 24 = 66

Answer : The two digit number is 42.

Answer 2

Given :

In a two digit number, digit at the tens place is twice the digit at units place. The number obtained by interchanging the digits is added to the original number, the sum is 66.

To Find :

The original number.

Solution :

Analysis :

Here we have form two linear equations with the help of the given information. Then solving the two equations simultaneously we can get the number.

Explanation :

Let the unit's digit be “x”.

Ten's digit be “2x”.

• Original no in expanded form is 10(2x) + x.
• Reversed no in expanded form is 10x + 2x

Now,

It is said that if the number obtained by interchanging the digits is added to the original number, the sum is 66.

☯ According to the question,

⇒ 10(2x) + x + 10x + 2x = 66

Expanding the brackets,

⇒ 20x + x + 10x + 2x = 66

⇒ 20x + 2x + 10x + x = 66

⇒ 22x + 11x = 66

⇒ 33x = 66

⇒ x = 66/33

⇒ x = 2

∴ x = 2.

The number :

• x = 2
• 2x = 2 × 2 = 4

Now , original number = 10(2x) + x

Orignal number = 10(4) + 2

Original number = 42

The original number is 42.

Verification :

LHS :

⇒ 10(2x) + x + 10x + 2x

Expanding the brackets,

⇒ 20x + x + 10x + 2x

Putting x = 2,

⇒ 20(2) + 2(2) + 10(2) + 2

⇒ 40 + 4 + 20 + 2

⇒ 44 + 22

⇒ 66

∴ 66.

RHS :

∴ 66.

∴ LHS = RHS.

• Hence verified.